3 4 Properties of Logarithmic Functions Copyright 2011

3. 4 Properties of Logarithmic Functions Copyright © 2011 Pearson, Inc.

What you’ll learn about n n Properties of Logarithms Change of Base Graphs of Logarithmic Functions with Base b Re-expressing Data … and why The applications of logarithms are based on their many special properties, so learn them well. Copyright © 2011 Pearson, Inc. Slide 3. 4 - 2

Properties of Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 3

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 4

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 5

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3. 4 - 6

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3. 4 - 7

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 - 8

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 - 9

Change-of-Base Formula for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 10

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3. 4 - 11

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3. 4 - 12

Example Transforming Logarithmic Graphs log x Copyright © 2011 Pearson, Inc. Slide 3. 4 - 13

Example Transforming Logarithmic Graphs Copyright © 2011 Pearson, Inc. Slide 3. 4 - 14

Example Transforming Logarithmic Graphs log x Since log x= Copyright © 2011 Pearson, Inc. Slide 3. 4 - 15

Quick Review Copyright © 2011 Pearson, Inc. Slide 3. 4 - 16

Quick Review Solutions Copyright © 2011 Pearson, Inc. Slide 3. 4 - 17